Art : Escher

Tesselations

"I cannot imagine what my life would be like if this problem had never occurred to me.
One might say that I am head over heels in love with it, and I still don't know why."
--Escher

A tessellation is a pattern of a shape with no spaces in between. Brick walls are a good example of a tesselation; each brick is the same shape and they all fit together. If we were to draw a wall, we would think of a single brick and then shift that forward horizontally, to create a single, infinitely long row of bricks. Then, we would take that row and move it up vertically and over horizontally to create another row, slightly displaced. If this were to go on and on, we would end up with an infinitely expansive wall of bricks. Escher creates a "brick wall" out of objects such as devils, horsemen, or fish.

Or as Escher himself said:"A plane, which should be considered limitless on all sides, can be filled with or divided into similar geometric figures that border each other on all sides without leaving any 'empty spaces'. This can be carried on to ininity..."



Here are some examples of different kinds of tesselations in Escher's work:




While this may look like a flock of butterflies, it is really groups of interlocking parallelograms that fill the picture. A single butterfly has been translated diagonally over and over again.



In this picture, there are interlocking rectangles of boats and fish. Here, the image is rotatated horizontally AND vertically, then shifted over.








The crabs are shifted forward vertically. Then, the whole line of crabs were rotated 180 degrees and moved over horizontally to form a new line of crabs facing the other way.







This picture represents one of Escher's more complex configurations. First, the fish is shifted forward horizontally to create an entire row of fish. Then, that row is glide reflected vertically AND in both directions diagonally.



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Page author: Alex Timbers